An operational amplifier is high gain amplifier usually

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Various op-amp ICs in 8-pin dual in-line packages ("DIPs")

An operational amplifier, which is often called an op-amp, is a DC-coupled high-gain
electronic voltage amplifier with differential inputs and, usually, a single output.[1]
Typically the output of the op-amp is controlled either by negative feedback, which
largely determines the magnitude of its output voltage gain, or by positive feedback,
which facilitates regenerative gain and oscillation. High input impedance at the input
terminals (ideally infinite) and low output impedance (ideally zero) are important typical

Op-amps are among the most widely used electronic devices today, being used in a vast
array of consumer, industrial, and scientific devices. Many standard IC op-amps cost only
a few cents in moderate production volume; however some integrated or hybrid
operational amplifiers with special performance specifications may cost over $100 US in
small quantities.

Modern designs are electronically more rugged than earlier implementations and some
can sustain direct short circuits on their outputs without damage.

The op-amp is one type of differential amplifier. Other types of differential amplifier
include the fully differential amplifier (similar to the op-amp, but with 2 outputs), the
instrumentation amplifier (usually built from 3 op-amps), the isolation amplifier (similar
to the instrumentation amplifier, but which works fine with common-mode voltages that
would destroy an ordinary op-amp), and negative feedback amplifier (usually built from
1 or more op-amps and a resistive feedback network).

Circuit notation

Circuit diagram symbol for an op-amp

The circuit symbol for an op-amp is shown to the right, where:

      V + : non-inverting input
      V − : inverting input
      Vout: output
      VS + : positive power supply
      VS − : negative power supply

The power supply pins (VS + and VS − ) can be labeled in different ways (See IC power
supply pins). Despite different labeling, the function remains the same — to provide
additional power for amplification of signal. Often these pins are left out of the diagram
for clarity, and the power configuration is described or assumed from the circuit.

The amplifier's differential inputs consist of V + input and a V − input, and generally the
op-amp amplifies only the difference in voltage between the two. This is called the
differential input voltage. Operational amplifiers are usually used with feedback loops
where the output of the amplifier would influence one of its inputs. The output voltage
and the input voltage it influences settles down to a stable voltage after being connected
for some time, when they satisfy the internal circuit of the op amp.

In its most common use, the op-amp's output voltage is controlled by feeding a fraction
of the output signal back to the inverting input. This is known as negative feedback. If
that fraction is zero (i.e., there is no negative feedback) the amplifier is said to be running
open loop and its output is the differential input voltage multiplied by the total gain of the
amplifier, as shown by the following equation:

where V + is the voltage at the non-inverting terminal, V − is the voltage at the inverting
terminal and G is the total open-loop gain of the amplifier.

Since the magnitude of the open-loop gain is typically very large, open-loop operation
results in op-amp saturation (see below in Nonlinear imperfections) unless the differential
input voltage is extremely small. Finley's law states that "When the inverting and non-
inverting inputs of an op-amp are not equal, its output is in saturation." Additionally, the
precise magnitude of this gain is not well controlled by the manufacturing process, and so
it is impractical to use an operational amplifier as a stand-alone differential amplifier.
Instead, op-amps are usually used in negative-feedback configurations.

Most single, dual and quad op-amps available have a standardized pin-out which permits
one type to be substituted for another without wiring changes. A specific op-amp may be
chosen for its open loop gain, bandwidth, noise performance, input impedance, power
consumption, or a compromise between any of these factors.

Ideal op-amp

Equivalent circuit of an operational amplifier.

Shown on the right is an example of an ideal operational amplifier. The main part in an
amplifier is the dependent voltage source that increases in relation to the voltage drop
across Rin, thus amplifying the voltage difference between V + and V − . Many uses have
been found for operational amplifiers and an ideal op-amp seeks to characterize the
physical phenomena that make op-amps useful.

Supply voltages Vcc + and Vcc − are used internally to implement the dependent voltage
sources. The positive source Vs + acts as an upper bound on the output, and the negative
source Vs − acts as a lower bound on the output. The internal Vs + and Vs − connections are
not shown here and will vary by implementation of the operational amplifier.

For any input voltages, an ideal op-amp has the following properties:

      Infinite open-loop gain (i.e., when doing theoretical analysis, limit should be
       taken as open loop gain Gopenloop goes to infinity)
      Infinite bandwidth (i.e., the frequency magnitude response is flat everywhere with
       zero phase shift).
      Infinite input impedance (i.e.,            , and so zero current flows from V + to V
       − )
      Zero input current (i.e., there is no leakage or bias current into the device)
      Zero input offset voltage (i.e., when the input terminals are shorted so that V + = V
       − , the output is a virtual ground).
      Infinite slew rate (i.e., the rate of change of the output voltage is unbounded) and
       power bandwidth (full output voltage and current available at all frequencies).
      Zero output impedance (i.e., Rout = 0, and so output voltage does not vary with
       output current)
      Zero noise
      Infinite Common-mode rejection ratio (CMRR)
      Infinite Power supply rejection ratio for both power supply rails.

Because of these properties, an op-amp can be modeled as a nullor

An operational amplifier is a high gain amplifier usually consisting of one or more
differential amplifier and usually followed by a level translator and an output stage.

The op-amp is a versatile device that can be used to amplify dc as well as ac input signal
and was originally designed for performing mathematical operations such as addition
,subtraction,multiplication and integration.Thus the name operational amplifier stems
from its original use for these mathematical operations and is abbreviated to op-amp.The
first op-amp was introduced by Fairchild semiconductor in 1963,its μA 702 which set the
stage for development of other IC op-amps

Internal Block Schematic of op-amp

The input stage is the dual input balanced output differential amplifier.This stage
generally provides most of the voltage gain of the amplifier and also establishes the input
resistance of the op-amp.The intermediate stage is usually another differential
amplifier,which is driven by the output of the first stage.On most amplifiers,the
intermediate stage is dual input,unbalanced output. Because of direct coupling,the dc
voltage at the output of the intermediate stage is well above ground
potential.Therefore,the level translator(shifting)circuits is used after the intermediate
stage downwards to zero volts with respect to ground.The final stage is usually a push
pull complementary symmetry amplifier output stage.The output stage increases the
voltage swing and raises the ground supplying capabilities of the op-amp.a well designed
output stage also provides low output resistance.

   Test Parameter     Typ.             Typical Description
                                Each input of an operational amplifier has a
                                certain amount of current that flows in or out
                                of it. This is basically the leakage current of
                                the input transistor, i.e., the base leakage
                                current if the input transistor is bipolar, or the
Input Bias Current      µA      gate leakage current if it is a FET. This
                                current is known as the input bias current,
                                and is ideally zero.
                                Example of an Actual Spec:
                                AD829: 3.3 µA typ.; 7 µA max.
                                This is simply the mismatch or difference
                                between the input bias currents flowing
Input Offset Current    nA      through the inputs. This is ideally zero.
                                Example of an Actual Spec:
                                AD829: 50 nA typ.; 500 nA max.
                                An ideal operational amplifier will give an
                                output of 0V if both of its inputs are shorted
                                together. A real-world op amp will have a
                                non-zero voltage output even if its inputs are
                                shorted together. This is the effect of its
                                input offset voltage, which is the slight
Input Offset Voltage    mV      voltage present across its inputs brought
                                about by its non-zero input offset current. In
                                essence, the input voltage offset is also the
                                voltage that needs to be applied across the
                                inputs of an op amp to make its output zero.
                                Example of an Actual Spec:
                                AD712C: 0.1 mV typ.; 0.3 mV max.
                                This is the ratio of the op amp's output
                                voltage to its differential input voltage without
Open-Loop Gain         V/mV     any external feedback.
                                Example of an Actual Spec:
                                AD712: 150 V/mV min.; 400 V/mV typ.
                                This is the product of the op amp's open-loop
                                voltage gain and the frequency at which it
Gain-Bandwidth                  was measured.
                                Example of an Actual Spec:
                                AD829: 750 MHz for Vs=+/-15V
                                This is the rate of change of the op amp's
                                voltage output over time when its gain is set
Slew Rate              V/µsec   to unity (Gain =1).
                                Example of an Actual Spec:
                                AD712: 16 V/µsec min.; 20 V/µsec typ.
                                This is the length of time for the output
                                voltage of an operational amplifier to
                                approach, and remain within, a certain
                                tolerance of its final value. This is usually
Settling Time           nsec    specified for a fast full-scale input step.
                                Example of an Actual Spec:
                                Settling time to 0.1% for a 10V step with
                                Vs=+/-15V: 90 nsec

Common Mode                     This is the ability of an operational amplifier
                        dB      to cancel out or reject any signals that are
Rejection (CMR)
                                common to both inputs, and amplify any
                                 signals that are differential between them.
                                 Common mode rejection is the logarithmic
                                 expression          of       CMRR,      i.e.,
                                 CMR=20logCMRR. CMRR is simply the ratio
                                 of the differential gain to the common-mode
                                 Example of an Actual Spec:
                                 AD829: 100 dB min.; 120 dB typ.
                               PSR is a measure of an op amp’s ability to
                               prevent its output from being affected by
                               noise or ripples at the power supply. It is
                               computed as the ratio of the change in the
Power Supply                   power supply voltage to the change in the op
                         dB    amp's output voltage (caused by the power
Rejection (PSR)
                               supply change). It is often expressed in dB.
                               Example of an Actual Spec:
                               AD829: 98 dB min.; 120 dB typ. for Vs=+/-
                               4.5V to +/-18V
                               An op amp will tend to oscillate at a
                               frequency wherein the loop phase shift
                               exceeds -180°, if this frequency is below the
                               closed-loop bandwidth. The closed-loop
                               bandwidth of a voltage-feedback op amp
                               circuit is equal to the op amp's bandwidth at
                               unity gain, divided by the circuit's closed loop
                               The phase margin of an op amp circuit is the
                               amount of additional phase shift at the closed
                               loop bandwidth required to make the circuit
                               unstable (i.e., phase shift + phase margin = -
                               180°). As phase margin approaches zero, the
Phase Margin           degrees loop phase shift approaches -180° and the op
                               amp circuit approaches instability.
                               Typically, values of phase margin much less
                               than 45° can cause problems such as
                               "peaking" in frequency response, and
                               overshoot or "ringing" in step response. In
                               order to maintain conservative phase margin,
                               the pole generated by capacitive loading
                               should be at least a decade above the
                               circuit's closed loop bandwidth.
                               Example of an Actual Spec:
                               AD847: 50 degrees
                               AD829: 60 degrees
                               This is the maximum voltage (negative or
                               positive) that can be applied at both inputs of
                               an operational amplifier at the same time,
Input Voltage Range,           with respect to the ground.
Common Mode                    Examples of Actual Specs:
                               AD712: +14.5V, -11.5 V typ. for Vs=+/-15 V;
                               AD844: +/- 10V for Vs=+/-15 V
                                 This is the maximum voltage (negative or
Input Voltage Range,             positive) that can be applied across the two
                          V      inputs of an operational amplifier.
                                 Example of an Actual Spec: AD712: +/-20V

Output Voltage Swing    +/-V     This is the maximum output voltage that the
                                 op amp can deliver without saturation or
                                   clipping for a given load and operating supply
                                   Example of an Actual Spec:
                                   +/-11V min.; +/-13V typ. for R=1K; Vs=+/-15V
                                   This is the small-signal resistance between
 Input Resistance or               the two inputs (both ungrounded) of an op
 Impedance,                M      amp.
 Differential                      Example of an Actual Spec:
                                   OP27C: 0.7 Mmin.; 4 M typ.
                                   Each input of an op amp has a resistance
                                   with respect to ground. The common mode
                                   input resistance of an op amp is the
 Input Resistance or               equivalent resistance value of the op amp's
 Impedance, Common         G      two input resistances in parallel. This is the
 Mode                              resistance of the two inputs shorted together
                                   with respect to ground.
                                   Example of an Actual Spec:
                                   OP27C: 2 G typ.
                                   This is the small-signal resistance or
                                   impedance between the output of an op amp
 Output Resistance or
                                  and ground.
                                   Example of an Actual Spec: AD844: 15
                                    typ., open loop
                                   This refers to the minimum and maximum
                                   values of supply voltages that the negative
                                   and positive supplies of an operational
 Power Supply Range         V      amplifier can accept.
                                   Example of an Actual Spec:
                                   AD712: +/- 4.5V min.; +/-18V max.
                                   This is the non-signal power supply current
                                   that the op amp will consume within a
                                   specified power supply voltage operating
 Quiescent Current         mA      range.
                                   Example of an Actual Spec:
                                   AD712: 5 mA typ.; 6.8 mA max. for Vs=+/-
                                   The total DC power supplied to the op amp
                                   minus the power delivered by the op amp to
 Total Power                       its load.
                                   Example of an Actual Spec:
                                   OP27: 90-100 mW typ.; 140-170 mW max.

Operational Amplifiers:

The operational amplifier is a direct-coupled high gain amplifier usable from 0 to over 1MH Z to which
feedback is added to control its overall response characteristic i.e. gain and bandwidth. The op-amp exhibits
the gain down to zero frequency.
Such direct coupled (dc) amplifiers do not use blocking (coupling and by pass) capacitors since these would
reduce the amplification to zero at zero frequency. Large by pass capacitors may be used but it is not
possible to fabricate large capacitors on a IC chip. The capacitors fabricated are usually less than 20 pf.
Transistor, diodes and resistors are also fabricated on the same chip.

Differential Amplifiers:

Differential amplifier is a basic building block of an op-amp. The function of a differential amplifier is to
amplify the difference between two input signals.

How the differential amplifier is developed? Let us consider two emitter-biased circuits as shown in fig. 1.

                                                       Fig. 1

The two transistors Q1 and Q2 have identical characteristics. The resistances of the circuits are equal, i.e.
RE1 = R E2, RC1 = R C2 and the magnitude of +VCC is equal to the magnitude of ?VEE. These voltages are
measured with respect to ground.

To make a differential amplifier, the two circuits are connected as shown in fig. 1. The two +VCC and ?VEE
supply terminals are made common because they are same. The two emitters are also connected and the
parallel combination of RE1 and RE2 is replaced by a resistance RE. The two input signals v1 & v2 are applied
at the base of Q1 and at the base of Q2. The output voltage is taken between two collectors. The collector
resistances are equal and therefore denoted by RC = RC1 = RC2.

Ideally, the output voltage is zero when the two inputs are equal. When v 1 is greater then v2 the output
voltage with the polarity shown appears. When v1 is less than v2, the output voltage has the opposite

The differential amplifiers are of different configurations.

The four differential amplifier configurations are following:

    1.   Dual input, balanced output differential amplifier.
    2.   Dual input, unbalanced output differential amplifier.
    3.   Single input balanced output differential amplifier.
    4.   Single input unbalanced output differential amplifier.
                                                     Fig. 2

These configurations are shown in fig. 2, and are defined by number of input signals used and the way an
output voltage is measured. If use two input signals, the configuration is said to be dual input, otherwise it is
a single input configuration. On the other hand, if the output voltage is measured between two collectors, it is
referred to as a balanced output because both the collectors are at the same dc potential w.r.t. ground. If the
output is measured at one of the collectors w.r.t. ground, the configuration is called an unbalanced output.

A multistage amplifier with a desired gain can be obtained using direct connection between successive
stages of differential amplifiers. The advantage of direct coupling is that it removes the lower cut off
frequency imposed by the coupling capacitors, and they are therefore, capable of amplifying dc as well as ac
input signals.
                          Real vs Ideal Op-amp
Readily available, inexpensive IC op-amps have characteristics which are reasonable
approximations of an ideal op-amp (data from Simpson):

These characteristics lead to the golden rules for op-amps. They all


This is the basic op-amp equation in which the output offset voltage is assumed to be
zero.The graphic representation of this equation is shown;where the output voltage ,Vo is
plotted against input difference voltage Vid,keeping gain A constant.The output voltage
cannot exceed the positive and negative saturation voltage.These saturation voltages are
specified by an output voltage swing ratings of an op-amp for given values of supply
voltages.The output voltage is directly proportional to the input difference voltage until it
reaches the saturation voltages and thereafter the output voltage remains constant.

This curve is called ideal voltage transfer curve

Open loop OPAMP Configuration:

In the case of amplifiers the term open loop indicates that no connection, exists between input and output
terminals of any type. That is, the output signal is not fedback in any form as part of the input signal.

In open loop configuration, The OPAMP functions as a high gain amplifier. There are three open loop
OPAMP configurations.
The Differential Amplifier:

Fig. 1, shows the open loop differential amplifier in which input signals vin1 and vin2 are applied to the positive
and negative input terminals.

                                                      Fig. 1

Since the OPAMP amplifies the difference the between the two input signals, this configuration is called the
differential amplifier. The OPAMP amplifies both ac and dc input signals. The source resistance Rin1 and Rin2
are normally negligible compared to the input resistance Ri. Therefore voltage drop across these resistances
can be assumed to be zero.


v1 = vin1 and v2 = vin2.

vo = Ad (vin1 ? vin2 )

where, Ad is the open loop gain.

The Inverting Amplifier:

If the input is applied to only inverting terminal and non-inverting terminal is grounded then it is called
inverting amplifier.This configuration is shown in fig. 2.

v1= 0, v2 = vin.

vo = -Ad vin
                                                      Fig. 2

The negative sign indicates that the output voltage is out of phase with respect to input 180 ° or is of
opposite polarity. Thus the input signal is amplified and inverted also.

The non-inverting amplifier:

In this configuration, the input voltage is applied to non-inverting terminals and inverting terminal is ground
as shown in fig. 3.

v1 = +vin           v2 = 0

vo = +Ad vin

This means that the input voltage is amplified by Ad and there is no phase reversal at the output.

                                                      Fig. 3

In all there configurations any input signal slightly greater than zero drive the output to saturation level. This
is because of very high gain. Thus when operated in open-loop, the output of the OPAMP is either negative
or positive saturation or switches between positive and negative saturation levels. Therefore open loop op-
amp is not used in linear applications.
Slew Rate of Op Amp Circuits
E.L. Dove, 2/13/2004
The slew rate (SR) is defined as the maximum rate of change of the output of an op amp
circuit. The SR in general describes the degradation effect on the high frequency response
of the active amplifier (one with an op amp) near or at the rated maximum output voltage
swing. This effect is generally due to the compensating capacitor and not to the transistor
circuits internal to the op amp. In short, the SR effect is due to the maximum supplied
current available for charging up the compensating capacitor.
We know that the current required to charge a capacitor is

I = c dv/dt
The Slew Rate is found from

SR=I dv/d tmax

Consider the following example. Suppose that the input signal to a 741-based unity gain
amplifier configuration is a 20kHz sine wave.
  What is the largest possible amplitude of the input signal to avoid distortion due to
The Slew Rate is found as the maximum of this derivative, or
dv0/dt = M 2pi f cos 2pift

SR= M 2pifM


Positive feedback configurations

Another typical configuration of op-amps is the positive feedback, which takes a fraction
of the output signal back to the non-inverting input. An important application of it is the
comparator with hysteresis (i.e., the Schmitt trigger).

Basic single stage amplifiers

Non-inverting amplifier

An op-amp connected in the non-inverting amplifier configuration
The general op-amp has two inputs and one output. The output voltage is a multiple of
the difference between the two inputs (some are made with floating, differential outputs):

G is the open-loop gain of the op-amp. The inputs are assumed to have very high
impedance; negligible current will flow into or out of the inputs. Op-amp outputs have
very low source impedance.

If the output is connected to the inverting input, after being scaled by a voltage divider:


                                            , where G > 0

Solving for Vout / Vin, we see that the result is a linear amplifier with gain:

If G is very large,      comes close to                     .

Inverting amplifier
Because it does not require a differential input, this negative feedback connection was the
most typical use of an op-amp in the days of analog computers.[citation needed] It remains
very popular,[citation needed] but many different configurations are possible, making it one of
the most versatile of all electronic building blocks.
An op-amp connected in the inverting amplifier configuration

By applying KCL at the inverting input,

However, because the input current into any operational amplifier is assumed to be zero,

and so

By applying KVL at the output,

However, because the operational amplifier is in a negative-feedback configuration, the
inverting input v − can be assumed to match the non-inverting input v + . In particular,

and so v − is a virtual ground. Therefore,

Hence, closed loop gain

        Some Variations:
            o A resistor is often inserted between the non-inverting input and ground (so
               both inputs "see" similar resistances), reducing the input offset voltage due
               to different voltage drops due to bias current, and may reduce distortion in
               some op-amps.
           o   A DC-blocking capacitor may be inserted in series with the input resistor
               when a frequency response down to DC is not needed and any DC voltage
               on the input is unwanted. That is, the capacitive component of the input
               impedance inserts a DC zero and a low-frequency pole that gives the
               circuit a bandpass or high-pass characteristic.

Other applications

      audio- and video-frequency pre-amplifiers and buffers
      voltage comparators
      differential amplifiers
      differentiators and integrators
      filters
      precision rectifiers
      precision peak detectors
      voltage and current regulators
      analog calculators
      analog-to-digital converters
      digital-to-analog converter
      voltage clamps
      oscillators and waveform generators

Limitations of real op-amps
Real op-amps can only approach this ideal: in addition to the practical limitations on slew
rate, bandwidth, offset and so forth mentioned above, real op-amp parameters are subject
to drift over time and with changes in temperature, input conditions, etc. Modern
integrated FET or MOSFET op-amps approximate more closely the ideal op-amp than
bipolar ICs where large signals must be handled at room temperature over a limited
bandwidth; input impedance, in particular, is much higher, although the bipolar op-amps
usually exhibit superior (i.e., lower) input offset drift and noise characteristics.

Where the limitations of real devices can be ignored, an op-amp can be viewed as a black
box with gain; circuit function and parameters are determined by feedback, usually
negative. IC op-amps as implemented in practice are moderately complex integrated
circuits; see the internal circuitry for the relatively simple 741 op-amp below, for

DC imperfections

Real operational amplifiers suffer from several non-ideal effects:

Finite gain
        Open-loop gain is defined as the amplification from input to output without any
        feedback applied. For mathematical calculations, the ideal open-loop gain is
        infinite; however, it is finite in real operational amplifiers. Typical devices exhibit
        open-loop DC gain ranging from 100,000 to over 1 million. So long as the loop
        gain (i.e., the product of open-loop and feedback gains) is very large, the circuit
        gain will be determined entirely by the amount of negative feedback (i.e., it will
        be independent of open-loop gain). In cases where closed-loop gain must be very
        high, the feedback gain will be very low, and the low feedback gain causes low
        loop gain; in these cases, the operational amplifier will cease to behave ideally.
Finite input impedance
        The input impedance of the operational amplifier is defined as the impedance
        between its two inputs. It is not the impedance from each input to ground. In the
        typical high-gain negative-feedback applications, the feedback ensures that the
        two inputs sit at the same voltage, and so the impedance between them is made
        artificially very high. Hence, this parameter is rarely an important design
        parameter. Because MOSFET-input operational amplifiers often have protection
        circuits that effectively short circuit any input differences greater than a small
        threshold, the input impedance can appear to be very low in some tests. However,
        as long as these operational amplifiers are used in a typical high-gain negative
        feedback application, these protection circuits will be inactive and the negative
        feedback will render the input impedance to be practically infinite. The input bias
        and leakage currents described below are a more important design parameter for
        typical operational amplifier applications.
Non-zero output impedance
        Low output impedance is important for low resistance loads; for these loads, the
        voltage drop across the output impedance of the amplifier will be significant.
        Hence, the output impedance of the amplifier reflects the maximum power that
        can be provided. Similarly, low-impedance outputs typically require high
        quiescent (i.e., idle) current in the output stage and will dissipate more power. So
        low-power designs may purposely sacrifice low-impedance outputs.
Input current
        Due to biasing requirements or leakage, a small amount of current (typically ~10
        nanoamperes for bipolar op-amps, tens of picoamperes for JFET input stages, and
        only a few pA for MOSFET input stages) flows into the inputs. When large
        resistors or sources with high output impedances are used in the circuit, these
        small currents can produce large unmodeled voltage drops. If the input currents
        are matched and the impedance looking out of both inputs are matched, then the
        voltages produced at each input will be equal. Because the operational amplifier
        operates on the difference between its inputs, these matched voltages will have no
        effect (unless the operational amplifier has poor CMRR, which is described
        below). It is more common for the input currents (or the impedances looking out
        of each input) to be slightly mismatched, and so a small offset voltage can be
        produced. This offset voltage can create offsets or drifting in the operational
        amplifier. It can often be nulled externally; however, many operational amplifiers
        include offset null or balance pins and some procedure for using them to remove
        this offset. Some operational amplifiers attempt to nullify this offset
Input offset voltage
      This voltage, which is what is required across the op-amp's input terminals to
      drive the output voltage to zero,[7][nb 1] is related to the mismatches in input bias
      current. In the perfect amplifier, there would be no input offset voltage. However,
      it exists in actual op-amps because of imperfections in the differential amplifier
      that constitutes the input stage of the vast majority of these devices. Input offset
      voltage creates two problems: First, due to the amplifier's high voltage gain, it
      virtually assures that the amplifier output will go into saturation if it is operated
      without negative feedback, even when the input terminals are wired together.
      Second, in a closed loop, negative feedback configuration, the input offset voltage
      is amplified along with the signal and this may pose a problem if high precision
      DC amplification is required or if the input signal is very small.[nb 2]
Common mode gain
      A perfect operational amplifier amplifies only the voltage difference between its
      two inputs, completely rejecting all voltages that are common to both. However,
      the differential input stage of an operational amplifier is never perfect, leading to
      the amplification of these identical voltages to some degree. The standard
      measure of this defect is called the common-mode rejection ratio (denoted
      CMRR). Minimization of common mode gain is usually important in non-
      inverting amplifiers (described below) that operate at high amplification.
Temperature effects
      All parameters change with temperature. Temperature drift of the input offset
      voltage is especially important.
Power-supply rejection
      The output of a perfect operational amplifier will be completely independent from
      ripples that arrive on its power supply inputs. Every real operational amplifier has
      a specified power supply rejection ratio (PSRR) that reflects how well the op-amp
      can reject changes in its supply voltage. Copious use of bypass capacitors can
      improve the PSRR of many devices, including the operational amplifier.

AC imperfections

The op-amp gain calculated at DC does not apply at higher frequencies. To a first
approximation, the gain of a typical op-amp is inversely proportional to frequency. This
means that an op-amp is characterized by its gain-bandwidth product. For example, an
op-amp with a gain bandwidth product of 1 MHz would have a gain of 5 at 200 kHz, and
a gain of 1 at 1 MHz. This low-pass characteristic is introduced deliberately, because it
tends to stabilize the circuit by introducing a dominant pole. This is known as frequency

Typical low cost, general purpose op-amps exhibit a gain bandwidth product of a few
megahertz. Specialty and high speed op-amps can achieve gain bandwidth products of
hundreds of megahertz. For very high-frequency circuits, a completely different form of
op-amp called the current-feedback operational amplifier is often used.

Other imperfections include:
     Finite bandwidth — all amplifiers have a finite bandwidth. This creates several
      problems for op amps. First, associated with the bandwidth limitation is a phase
      difference between the input signal and the amplifier output that can lead to
      oscillation in some feedback circuits. The internal frequency compensation used
      in some op amps to increase the gain or phase margin intentionally reduces the
      bandwidth even further to maintain output stability when using a wide variety of
      feedback networks. Second, reduced bandwidth results in lower amounts of
      feedback at higher frequencies, producing higher distortion, noise, and output
      impedance and also reduced output phase linearity as the frequency increases.
     Input capacitance — most important for high frequency operation because it
      further reduces the open loop bandwidth of the amplifier.
     Common mode gain — See DC imperfections, above.

Nonlinear imperfections

     Saturation — output voltage is limited to a minimum and maximum value close to
      the power supply voltages.[nb 3] Saturation occurs when the output of the amplifier
      reaches this value and is usually due to:
          o In the case of an op-amp using a bipolar power supply, a voltage gain that
              produces an output that is more positive or more negative than that
              maximum or minimum; or
          o In the case of an op-amp using a single supply voltage, either a voltage
              gain that produces an output that is more positive than that maximum, or a
              signal so close to ground that the amplifier's gain is not sufficient to raise
              it above the lower threshold.[nb 4]
     Slewing — the amplifier's output voltage reaches its maximum rate of change.
      Measured as the slew rate, it is usually specified in volts per microsecond. When
      slewing occurs, further increases in the input signal have no effect on the rate of
      change of the output. Slewing is usually caused by internal capacitances in the
      amplifier, especially those used to implement its frequency compensation.
     Non-linear transfer function — The output voltage may not be accurately
      proportional to the difference between the input voltages. It is commonly called
      distortion when the input signal is a waveform. This effect will be very small in a
      practical circuit if substantial negative feedback is used.

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